Question

write a coordinate rule for the composition.
$(x,y)\to(\square,\square)$

Explanation:

Step1: Find the coordinates of a point in the original figure and its image

Let's take point \(Y\). The coordinates of \(Y\) are \((1,2)\). The coordinates of its image (say in the larger figure) need to be determined.

Step2: Analyze the transformation

Looking at the grid, if we assume a dilation (since the figure is scaled). If we consider the ratio of the sides. Let's check another point. Suppose \(Z=(2, - 1)\). If we assume a dilation factor \(k = 2\).
For a point \((x,y)\) under dilation with scale factor \(k\), the rule is \((x,y)\to(kx,ky)\)

Answer:

\((x,y)\to(2x,2y)\)